Answers

Wish- You're saying magic words in your head (or upon some external object) to make it happen.

Examples:

"I expect that tomorrow it will rain. I expect this because the local meteorologist has come to the same conclusion and because a tropical storm is moving up from the south."

"I hope I'll be able to see my mother one last time before she dies. I'm driving as fast as I can to the hospital, but she doesn't have much time left."

"I wish for a million dollars. Since I wished to the north star this time, I should get lucky!"

Obviously, "expecting" is little more than "reasonably predicting". "Hoping" is grounded in reality, knowing that you can't change the outcome of an event but desiring that it works out like you've envisioned. "Wishing" is lofty and unreasonable, seeing as magic, you know, isn't real.

However, people will occasionally use "wish" when they actually mean "hope", like, "Best wishes on your job interview!", and vice versa with "hope" and "wish", like, "Now that I flung a penny into the wishing well, I hope that I meet the man of my dreams on the subway tonight!" They're not the same word, but colloquially you can get away with treating them as synonyms and then figuring out what a person ACTUALLY means through context; if the thing they're hoping/wishing for is reasonable but uncertain, then it's "hope", and if the thing they're hoping/wishing for is absurd and highly implausible, then it's "wish".